arXiv subjects

Chris Sherlock

Publications and source records attributed to Chris Sherlock.

At least 19 recordsLinked to original sources

arXiv2026

Robust, partially alive particle Metropolis-Hastings via the Frankenfilter

When a hidden Markov model permits the conditional likelihood of an observation given the hidden process to be zero, all particle simulations from one observation time to the next could produce zeros. If so, the filtering distribution cannot be estimated and the estimated parameter likelihood is zero. The alive particle filter addresses this by simulating a random number of particles for each inter-observation interval, stopping after a target number of non-zero conditional likelihoods. For outlying observations or poor parameter values, a non-zero result can be extremely unlikely, and computational costs prohibitive. We introduce the Frankenfilter, a principled, partially alive particle filter that targets a user-defined amount of success whilst fixing lower and upper bounds on the number of simulations. The Frankenfilter produces unbiased estimators of the likelihood, suitable for pseudo-marginal Metropolis--Hastings (PMMH). We demonstrate that PMMH with the Frankenfilter is more robust to outliers and mis-specified initial parameter values than PMMH using standard particle filters, and is typically at least 2-3 times more efficient. We also provide advice for choosing the amount of success. In the case of n exact observations, this is particularly simple: target n successes.

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arXiv2025

Nested ensemble Kalman filter for static parameter inference in nonlinear state-space models

The ensemble Kalman filter (EnKF) is a popular technique for performing inference in state-space models (SSMs), particularly when the dynamic process is high-dimensional. Unlike reweighting methods such as sequential Monte Carlo (SMC, i.e. particle filters), the EnKF leverages either the linear Gaussian structure of the SSM or an approximation thereof, to maintain diversity of the sampled latent states (the so-called ensemble members) via shifting-based updates. Joint parameter and state inference using an EnKF is typically achieved by augmenting the state vector with the static parameter. In this case, it is assumed that both parameters and states follow a linear Gaussian state-space model, which may be unreasonable in practice. In this paper, we combine the reweighting and shifting methods by replacing the particle filter used in the SMC^2 algorithm of Chopin et al. (2013), with the ensemble Kalman filter. Hence, parameter particles are weighted according to the estimated observed-data likelihood from the latest observation computed by the EnKF, and particle diversity is maintained via a resample-move step that targets the marginal parameter posterior under the EnKF. Extensions to the resulting algorithm are proposed, such as the use of a delayed acceptance kernel in the rejuvenation step and incorporation of nonlinear observation models. We illustrate the resulting methodology via several applications.

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arXiv2025

MCMC for State Space models

A state-space model is a time-series model that has an unobserved latent process from which we take noisy measurements over time. The observations are conditionally independent given the latent process and the latent process itself is Markovian. These properties lead to simplifications for the conditional distribution of the latent process given the parameters and the observations. This chapter looks at how we can leverage the properties of state-space models to construct efficient MCMC samplers. We consider a range of Gibbs-sampler schemes, including those which use the forward-backward algorithm to simulate from the full conditional of the latent process given the parameters. For models where the forward-backward algorithm is not applicable we look at particle MCMC algorithms that, given the parameters, use particle filters to approximately simulate from the latent process or estimate the likelihood of the observations. Throughout, we provide intuition and informally discuss theory about the properties of the model that impact the efficiency of the different algorithms and how approaches such as reparameterization can improve mixing.

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arXiv2024

Variance bounds and robust tuning for pseudo-marginal Metropolis--Hastings algorithms

The general applicability and ease of use of the pseudo-marginal Metropolis--Hastings (PMMH) algorithm, and particle Metropolis--Hastings in particular, makes it a popular method for inference on discretely observed Markovian stochastic processes. The performance of these algorithms and, in the case of particle Metropolis--Hastings, the trade off between improved mixing through increased accuracy of the estimator and the computational cost were investigated independently in two papers, both published in 2015. Each suggested choosing the number of particles so that the variance of the logarithm of the estimator of the posterior at a fixed sensible parameter value is approximately 1. This advice has been widely and successfully adopted. We provide new, remarkably simple upper and lower bounds on the asymptotic variance of PMMH algorithms. The bounds explain how blindly following the 2015 advice can hide serious issues with the algorithm and they strongly suggest an alternative criterion. In most situations our guidelines and those from 2015 closely coincide; however, when the two differ it is safer to follow the new guidance. An extension of one of our bounds shows how the use of correlated proposals can fundamentally shift the properties of pseudo-marginal algorithms, so that asymptotic variances that were infinite under the PMMH kernel become finite.

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arXiv2024

Bayesian inference for the Markov-modulated Poisson process with an outcome process

In medical research, understanding changes in outcome measurements is crucial for inferring shifts in health conditions. However, traditional methods often struggle with large, irregularly longitudinal data and fail to account for the tendency of individuals in poorer health to interact more frequently with the healthcare system. Additionally, clinical data can lack information on terminating events like death. To address these challenges, we start from the continuous-time hidden Markov model which models observed data as outcomes influenced by latent health states. Our extension incorporates a point process to account for the impact of health states on observation timings and includes a "death" state to model unobserved terminating events through a Poisson process, where transition rates depend on the latent health state. This approach captures both the severity of the disease and the timing of healthcare interactions. We present an exact Gibbs sampler procedure that alternates between sampling the latent health state paths and the model parameters. By including the "death" state, we mitigate biases in parameter estimation that would arise from solely modelling "live" health states. Simulation studies demonstrate that the proposed Gibbs sampler performs effectively. We apply our method to Canadian healthcare data, offering valuable insights for healthcare management.

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arXiv2024

Metropolis--Hastings with Scalable Subsampling

The Metropolis-Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement. However, in the context of Bayesian inference for large datasets, evaluating the likelihood on the full data for thousands of iterations until convergence can be prohibitively expensive. This paper introduces a new subsample MH algorithm that satisfies detailed balance with respect to the target posterior and utilises control variates to enable exact, efficient Bayesian inference on datasets with large numbers of observations. Through theoretical results, simulation experiments and real-world applications on certain generalised linear models, we demonstrate that our method requires substantially smaller subsamples and is computationally more efficient than the standard MH algorithm and other exact subsample MH algorithms.

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arXiv2024

Scalable Monte Carlo for Bayesian Learning

This book aims to provide a graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC) algorithms, as applied broadly in the Bayesian computational context. Most, if not all of these topics (stochastic gradient MCMC, non-reversible MCMC, continuous time MCMC, and new techniques for convergence assessment) have emerged as recently as the last decade, and have driven substantial recent practical and theoretical advances in the field. A particular focus is on methods that are scalable with respect to either the amount of data, or the data dimension, motivated by the emerging high-priority application areas in machine learning and AI.

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arXiv2023

Fast return-level estimates for flood insurance via an improved Bennett inequality for random variables with differing upper bounds

Insurance losses due to flooding can be estimated by simulating and then summing losses over a large number of locations and a large set of hypothetical years of flood events. Replicated realisations lead to Monte Carlo return-level estimates and associated uncertainty. The procedure, however, is highly computationally intensive. We develop and use a new, Bennett-like concentration inequality to provide conservative but relatively accurate estimates of return levels. Bennett's inequality accounts for the different variances of each of the variables in a sum but uses a uniform upper bound on their support. Motivated by the variability in the total insured value of risks within a portfolio, we incorporate both individual upper bounds and variances and obtain tractable concentration bounds. Simulation studies and application to a representative portfolio demonstrate a substantial tightening compared with Bennett's bound. We then develop an importance-sampling procedure that repeatedly samples annual losses from the distributions implied by each year's concentration inequality, leading to conservative estimates of the return levels and their uncertainty using orders of magnitude less computation. This enables a simulation study of the sensitivity of the predictions to perturbations in quantities that are usually assumed fixed and known but, in truth, are not.

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arXiv2022

Scalable couplings for the random walk Metropolis algorithm

There has been a recent surge of interest in coupling methods for Markov chain Monte Carlo algorithms: they facilitate convergence quantification and unbiased estimation, while exploiting embarrassingly parallel computing capabilities. Motivated by these, we consider the design and analysis of couplings of the random walk Metropolis algorithm which scale well with the dimension of the target measure. Methodologically, we introduce a low-rank modification of the synchronous coupling that is provably optimally contractive in standard high-dimensional asymptotic regimes. We expose a shortcoming of the reflection coupling, the state of the art at the time of writing, and we propose a modification which mitigates the issue. Our analysis bridges the gap to the optimal scaling literature and builds a framework of asymptotic optimality which may be of independent interest. We illustrate the applicability of our proposed couplings, and the potential for extending our ideas, with various numerical experiments.

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arXiv2022

SwISS: A Scalable Markov chain Monte Carlo Divide-and-Conquer Strategy

Divide-and-conquer strategies for Monte Carlo algorithms are an increasingly popular approach to making Bayesian inference scalable to large data sets. In its simplest form, the data are partitioned across multiple computing cores and a separate Markov chain Monte Carlo algorithm on each core targets the associated partial posterior distribution, which we refer to as a sub-posterior, that is the posterior given only the data from the segment of the partition associated with that core. Divide-and-conquer techniques reduce computational, memory and disk bottle-necks, but make it difficult to recombine the sub-posterior samples. We propose SwISS: Sub-posteriors with Inflation, Scaling and Shifting; a new approach for recombining the sub-posterior samples which is simple to apply, scales to high-dimensional parameter spaces and accurately approximates the original posterior distribution through affine transformations of the sub-posterior samples. We prove that our transformation is asymptotically optimal across a natural set of affine transformations and illustrate the efficacy of SwISS against competing algorithms on synthetic and real-world data sets.

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arXiv2022

Accelerating inference for stochastic kinetic models

Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are modelled using a continuous-time stochastic process, and, depending on the application area of interest, this will typically take the form of a Markov jump process or an It\^o diffusion process. Widespread use of these models is typically precluded by their computational complexity. In particular, performing exact fully Bayesian inference in either modelling framework is challenging due to the intractability of the observed data likelihood, necessitating the use of computationally intensive techniques such as particle Markov chain Monte Carlo (particle MCMC). It is proposed to increase the computational and statistical efficiency of this approach by leveraging the tractability of an inexpensive surrogate derived directly from either the jump or diffusion process. The surrogate is used in three ways: in the design of a gradient-based parameter proposal, to construct an appropriate bridge and in the first stage of a delayed-acceptance step. The resulting approach, which exactly targets the posterior of interest, offers substantial gains in efficiency over a standard particle MCMC implementation.

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arXiv2022

Centered plug-in estimation of Wasserstein distances

The plug-in estimator of the squared Euclidean 2-Wasserstein distance is conservative, however due to its large positive bias it is often uninformative. We eliminate most of this bias using a simple centering procedure based on linear combinations. We construct a pair of centered plug-in estimators that decrease with the true Wasserstein distance, and are therefore guaranteed to be informative, for any finite sample size. Crucially, we demonstrate that these estimators can often be viewed as complementary upper and lower bounds on the squared Wasserstein distance. Finally, we apply the estimators to Bayesian computation, developing methods for estimating (i) the bias of approximate inference methods and (ii) the convergence of MCMC algorithms.

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arXiv2021

The Apogee to Apogee Path Sampler

Amongst Markov chain Monte Carlo algorithms, Hamiltonian Monte Carlo (HMC) is often the algorithm of choice for complex, high-dimensional target distributions; however, its efficiency is notoriously sensitive to the choice of the integration-time tuning parameter, $T$. When integrating both forward and backward in time using the same leapfrog integration step as HMC, the set of local maxima in the potential along a path, or apogees, is the same whatever point (position and momentum) along the path is chosen to initialise the integration. We present the Apogee to Apogee Path Sampler (AAPS), which utilises this invariance to create a simple yet generic methodology for constructing a path, proposing a point from it and accepting or rejecting that proposal so as to target the intended distribution. We demonstrate empirically that AAPS has a similar efficiency to HMC but is much more robust to the setting of its equivalent tuning parameter, the number of apogees that the path crosses.

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arXiv2020

Augmented pseudo-marginal Metropolis-Hastings for partially observed diffusion processes

We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying It\^o stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our starting point is a state-of-the-art correlated pseudo-marginal Metropolis-Hastings algorithm, that uses correlated particle filters to induce strong and positive correlation between successive likelihood estimates. However, unless the measurement error or the dimension of the SDE is small, correlation can be eroded by the resampling steps in the particle filter. We therefore propose a novel augmentation scheme, that allows for conditioning on values of the latent process at the observation times, completely avoiding the need for resampling steps. We integrate over the uncertainty at the observation times with an additional Gibbs step. Connections between the resulting pseudo-marginal scheme and existing inference schemes for diffusion processes are made, giving a unified inference framework that encompasses Gibbs sampling and pseudo marginal schemes. The methodology is applied in three examples of increasing complexity. We find that our approach offers substantial increases in overall efficiency, compared to competing methods.

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arXiv2019

Recruitment prediction for multi-centre clinical trials based on a hierarchical Poisson-gamma model: asymptotic analysis and improved intervals

We analyse predictions of future recruitment to a multi-centre clinical trial based on a maximum-likelihood fitting of a commonly used hierarchical Poisson-Gamma model for recruitments at individual centres. We consider the asymptotic accuracy of quantile predictions in the limit as the number of recruitment centres grows large and find that, in an important sense, the accuracy of the quantiles does not improve as the number of centres increases. When predicting the number of further recruits in an additional time period, the accuracy degrades as the ratio of the additional time to the census time increases, whereas when predicting the amount of additional time to recruit a further $n^+_\bullet$ patients, the accuracy degrades as the ratio of $n^+_\bullet$ to the number recruited up to the census period increases. Our analysis suggests an improved quantile predictor. Simulation studies verify that the predicted pattern holds for typical recruitment scenarios in clinical trials and verify the much improved coverage properties of prediction intervals obtained from our quantile predictor. In the process of extending the applicability of our methodology, we show that in terms of the accuracy of all integer moments it is always better to approximate the sum of independent gamma random variables by a single gamma random variable matched on the first two moments than by the moment-matched Gaussian available from the central limit theorem.

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arXiv2019

Exact Bayesian inference for discretely observed Markov Jump Processes using finite rate matrices

We present new methodologies for Bayesian inference on the rate parameters of a discretely observed continuous-time Markov jump processes with a countably infinite state space. The usual method of choice for inference, particle Markov chain Monte Carlo (particle MCMC), struggles when the observation noise is small. We consider the most challenging regime of exact observations and provide two new methodologies for inference in this case: the minimal extended state space algorithm (MESA) and the nearly minimal extended state space algorithm (nMESA). By extending the Markov chain Monte Carlo state space, both MESA and nMESA use the exponentiation of finite rate matrices to perform exact Bayesian inference on the Markov jump process even though its state space is countably infinite. Numerical experiments show improvements over particle MCMC of between a factor of three and several orders of magnitude.

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arXiv2019

Interim recruitment prediction for multi-centre clinical trials

We introduce a general framework for monitoring, modelling, and predicting the recruitment to multi-centre clinical trials. The work is motivated by overly optimistic and narrow prediction intervals produced by existing time-homogeneous recruitment models for multi-centre recruitment. We first present two tests for detection of decay in recruitment rates, together with a power study. We then introduce a model based on the inhomogeneous Poisson process with monotonically decaying intensity, motivated by recruitment trends observed in oncology trials. The general form of the model permits adaptation to any parametric curve-shape. A general method for constructing sensible parameter priors is provided and Bayesian model averaging is used for making predictions which account for the uncertainty in both the parameters and the model. The validity of the method and its robustness to misspecification are tested using simulated datasets. The new methodology is then applied to oncology trial data, where we make interim accrual predictions, comparing them to those obtained by existing methods, and indicate where unexpected changes in the accrual pattern occur.

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arXiv2019

Hug and Hop: a discrete-time, non-reversible Markov chain Monte-Carlo algorithm

We introduced the Hug and Hop Markov chain Monte Carlo algorithm for estimating expectations with respect to an intractable distribution. The algorithm alternates between two kernels: Hug and Hop. Hug is a non-reversible kernel that repeatedly applies the bounce mechanism from the recently proposed Bouncy Particle Sampler to produce a proposal point far from the current position, yet on almost the same contour of the target density, leading to a high acceptance probability. Hug is complemented by Hop, which deliberately proposes jumps between contours and has an efficiency that degrades very slowly with increasing dimension. There are many parallels between Hug and Hamiltonian Monte Carlo using a leapfrog integrator, including the order of the integration scheme, however Hug is also able to make use of local Hessian information without requiring implicit numerical integration steps, and its performance is not terminally affected by unbounded gradients of the log-posterior. We test Hug and Hop empirically on a variety of toy targets and real statistical models and find that it can, and often does, outperform Hamiltonian Monte Carlo.

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